Asymptotic stability and capacity results for a broad family of power adjustment rules: Expanded discussion

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dc.creatorRodriguez, Virgilio
dc.creatorMathar, Rudolf
dc.creatorSchmeink, Anke
dc.date2009-01-05
dc.date.accessioned2026-07-07T12:24:51Z
dc.date.available2026-07-07T12:24:51Z
dc.descriptionIn any wireless communication environment in which a transmitter creates interference to the others, a system of non-linear equations arises. Its form (for 2 terminals) is p1=g1(p2;a1) and p2=g2(p1;a2), with p1, p2 power levels; a1, a2 quality-of-service (QoS) targets; and g1, g2 functions akin to "interference functions" in Yates (JSAC, 13(7):1341-1348, 1995). Two fundamental questions are: (1) does the system have a solution?; and if so, (2) what is it?. (Yates, 1995) shows that IF the system has a solution, AND the "interference functions" satisfy some simple properties, a "greedy" power adjustment process will always converge to a solution. We show that, if the power-adjustment functions have similar properties to those of (Yates, 1995), and satisfy a condition of the simple form gi(1,1,...,1)<1, then the system has a unique solution that can be found iteratively. As examples, feasibility conditions for macro-diversity and multiple-connection receptions are given. Informally speaking, we complement (Yates, 1995) by adding the feasibility condition it lacked. Our analysis is based on norm concepts, and the Banach's contraction-mapping principle.
dc.description9 pages; 3 figures
dc.identifierhttps://arxiv.org/abs/0901.0573
dc.identifierhttp://arxiv.org/abs/0901.0573
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/214449
dc.subjectInformation Theory
dc.subjectFunctional Analysis
dc.subject94A05; 91A80
dc.titleAsymptotic stability and capacity results for a broad family of power adjustment rules: Expanded discussion
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